Classical mathematical morphology is a method of nonlinear processing of images (originally) and now also signals, based on filtering of the images with simple geometrical figures. Examples of such figures may include circles, ellipses, squares, rectangles, etc. In general, four fundamental operations used in classical mathematical morphology constitute a “language” of morphological analysis. These fundamental operations are dilation, erosion, opening, and closure.
The application of these operations, as well as selecting the correct length scale(s) for the simple geometrical figures used for filtering, generally requires significant expertise in a variety of mathematical areas such as set theory, lattice theory, topology, and random functions. In order to achieve a desired result, quite often an application of a complex sequence of such operations is required, which makes this approach to “filtering with simple geometrical figures” not only a science, but rather, an art in itself.
General criteria are typically not available classical mathematical morphology formulations related to development of such sequences as well as how to terminate the work of a given algorithm. In addition, classical mathematical morphology was originally developed for binary images and later on generalized for grayscale images. Proposals are presently being made for processing of color images using classical mathematical morphology only now, some 50 years after the discovery of mathematical morphology.
There is a need for methods and apparatuses that use new and different types of mathematical morphological analysis that can be applied in a more straightforward manner and be more generally applied to signals in single and multiple dimensions rather than just 2 dimensions.